Quant Boosters  Vikas Saini  Set 1

let 6th month he had a sale of z.
6435+6927+6855+7230+6562+z = 6 x 6500
= > 34009 + z = 39000
= > z = 4991.Short approach :
let's take 6500 as base.
6500(65+427+355+730+62)
=6500  (1509)
= 4991.

Q6) The average weight of boys in a school is 47 and girls is 42. If there are 6 more boys than girls and average weight of all class is 44.8. How many students are in the class?

let no of girls = a
no of boys = a+6
47(a+6)+42a = 44.8(a+a+6)
47a+42a+282 = 44.8(2a+6)
89a + 282 = 89.6a + 268.8
0.6 a = 13.2
a = 22.
a+6 = 28.
total = 22+28 = 50.Short approach :
average of all class=44.8.
ratio of boys & girls= (4744.8 ):(44.842)=2.2:2.8.
(2.82.2)x=6
x=10.
total students= (2.2+2.8 )x10=50

Q7) Average weight of 11 players is increased by 1kg. When one player of team weighing 55kg is replaced by new player. Find weight of new player

Average weight of each player = a.
weight of new player = k.
11a  55 + k = 11(a+1)
k  55 = 11
k = 66.Short approach :
weight of new player = 55 + 1 x 11 = 66.

Q8) The average of 71 results is 48. If the average of first 59 results is 46 and that of the last 11 is 52 then find the 60th result.

71 x 48 = 59 x 46 + 11 x 52 + 60th
= > 60th value = 71 x 48  59 x 46  11 x 52.
= > 60th value = 122.Short approach :
We take 48 as base.
59 results average is 2 (from base)
11 results average is +4 (from base)
So 59 x (2) + 11 x 4 = 74.
To get 60th value this value should be decrease from base.
Hence 60th value = 48  (74) = 122.

Q9) The average of 50 numbers is 38. If two numbers, namely 45 & 55 are discarded then what is the average of remaining numbers ?

Total = 50 x 38 = 1900.
two numbers discarded (45,55)
new total = 19004555 = 1800.
new average = 1800 / 48 = 37.5Short approach :
The average of 50 numbers is 38.
so if we discarded two number then to maintain average of 38,value should be decreased by 2 x 38 = 76.
but here value decreased by 100.
So 10076 = 24.
There is 48 numbers.
so every number value will be decreased by 24/48 = 0.5
new average = 38  0.5 = 37.5.

Q10) The average runs of Rohit & Dhawan is 280. The average runs of Virat & Rahane is 200. What is the average of each of them.

Rohit + Dhawan = 2 x 280 = 560.
Virat + Rahane = 2 x 200 = 400.
Total runs = 560 + 400 = 960.
Average = 960 / 4 = 240.Short approach :
Take average of any two
let we take Rohit & Dhawan,which is nothing but 280.(base)
now average of virat & rahane 200.
which is 80 (from base)
Average = 280  (80/2)
= 280  40
= 240.We can solve it by take 200 too..
base = 200.
average of Rohit & Dhawan is +80(from base).
average = 200 + (80/2)
= 240.
Here divided by 2, because that is average of two person..

Q11) The average weight of a class of 29 students is 40 kg. If the weight of teacher be included,the average rises by 500gm. What is the weight of the teacher ?

previous weight of class = 29 x 40 = 1160 kg.
new weight (including teacher) = 30 x 40.5 = 1215.
Teacher's weight = 1215  1160 = 55 kg.Short approach :
base = 40.
including teacher average increased by 0.5 kg.
Teacher's weight = 40 + 30 x 0.5
= 40 + 15
= 55 kg.

Q12) By selling 18 oranges profit is equal to SP of 3 oranges. Find profit percentage.

Sp of 1 orange = x.
cp of 1 orange = y.
18x – 18y = 3x
= > 18 y = 15 x.
Profit percentage = (3x/18y)x100
= (3x/15x)x100
= 20%.Short approach :
Profit percentage = [profit (quantity) / (Total quantity – profit)] x 100
= [(3)/(183)] x 100
= [3/15] x 100
= 20%

Q13) By selling 18 chocolates, vendor loss selling price of 2 chocolates. Find loss percentage.

sp of 1 chocolate = x
cp of 1 chocolate = y
18 y – 18 x = 2x.
18 y = 20 x.
Loss percentage = (2x/18 y) x 100
= (2x/20x)x100
= 10%.Short approach :
Loss percentage = [Loss (quantity) / (Total quantity + loss) ] x 100
= [ 2 / (18+2) ] x 100
= 10%.

Q14) On selling an article for rs 576 a trader losses 4%. In order to gain 25/6 % , he must sell article for
a. 655 rs
b. 676 rs
c. 625 rs
d. 600 rs.

Cost price = [576 / (100 – 4)] x 100 = 600 rs.
Selling price = 600 x (1 + 25/(6 x 100) = 625.Short approach :
Direct formula to find sp in such problems
= previous selling price x 100 x (1+ gain percent)/(1 – loss percent)
= 576 x 100 x (1+25/600)/(1 – 4/100)
= 625 rs.

Q15) A goldsmith has 361 rings of gold. He sells some of them at a loss of 4% and rest at a profit of 15%. Overall profit is 8%. Find no of rings sold at profit of 15%.